The Mystery of Power Zero
Why does any number raised to the power of 0 equal 1? Let's find out by dividing.
Equation
y = x^2
Graph
Table
| x | y |
|---|---|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
What this lesson covers
What you do
You shape the function y = x^n and watch the graph answer.
Challenges to clear
- Verify that when n=0, y=1 for x=2
- Verify that when n=0, y=1 for x=5
- Slide n down to 0. Whatever x is, x⁰ collapses to 1 — the curve goes completely flat.
- So only the multiplier is left. Slide a until x = 5 reads 3 — and every other row reads 3 too, because x⁰ contributed nothing but 1.
Check yourself
Why is any non-zero number raised to the power of 0 equal to 1?
- Because x^n / x^n = 1, and using the quotient rule x^(n-n) = x^0, so x^0 must be 1. — correct
- Because 0 is the additive identity, so it resets the value to 1.
- Because multiplying by 0 always results in 1.
- It is undefined for all numbers.
Think about it
- Set the exponent n to 0. What happens to the y-values as x changes?